Medtronic, the world's biggest medical devices maker by sales, will buy Ireland-based rival Covidien in a $42.9 billion agreement that could increase concerns about the rush of U.S. companies striking deals to cut their tax bills.

The deal, announced late Sunday, involves Medtronic paying $35.19 in cash and 0.956 of an ordinary share of Medtronic to Covidien shareholders - a premium of 29 percent to the Ireland-based company's closing stock price on Friday.

"This acquisition will allow Medtronic to reach more patients, in more ways and in more places," Medtronic Chairman and CEO Omar Ishrak said in a statement:

Minneapolis-based Medtronic will create two new, Irish-listed companies called New Medtronic and New Medtronic Sub through which it will channel the transaction. As well as saving on Medtronic's tax bill, the acquisition is expected to deliver around $850 million of annual pretax savings by the end of 2018.

"To finance the deal, they have some $13 billion to $14 billion in cash trapped overseas. They wanted to free that up to use that," former Medtronic Chairman and CEO Bill George told CNBC on Monday.

The U.S. company had also been linked to a potential bid for U.K.-listed Smith & Nephew.

Ireland's corporate tax rate of 12.5 percent is substantially lower than the U.K.'s 21 percent and the 35 percent in the U.S. Covidien itself is historically based mainly in Massachusetts, but moved its headquarters to Ireland for tax reasons in 2009.

Medtronic is the latest U.S. company to do a "tax inversion"—move its base overseas for tax purposes, so that overseas revenues will be taxed at a lower rate. This kind of move particularly suits pharmaceutical companies because they tend to be cash-rich and generate a significant amount of their revenues overseas.

George, who has been against inversions, said this one is different. "They are not doing it for tax savings. Pfizer is looking to cut its tax," he said, noting that the tax rate for Medtronic and Covidien is already below the U.K.'s 21 percent. "There is not tax-rate savings."

Pfizer had been pursuing U.K. drug-maker AstraZeneca before deciding to abandon its bid because of opposition. But that $116 billion offer raised eyebrows on Capitol Hill, spurring U.S. lawmakers to talk about how to close the tax inversion loophole.